Use the command Select to find all integers x in the list $r=Range[16]$ such that $Mod[x^4,17]=-1$ and also try doing it by cases command

Question

My try:

r = Range[16];

Select[r, Mod[x^4,17] = -1]

but it doesn't work.

How can I do it?

Answer 1

Select[Range[16],
       Function[x,Mod[x^4+1,17]==0]]
(* {2,8,9,15} *)

Alternative syntax:

Select[Range[16],
       x |-> Mod[x^4+1,17] == 0]
(* {2,8,9,15} *)

Another solution using Pick:

With[{r=Range[16]},
  Pick[r,Mod[r^4+1,17],0]]
(* {2,8,9,15} *)

Answer 2

PowerModList[-1, 1/4, 17]

{2, 8, 9, 15}

Answer 3

Solve[x^4 == -1, Modulus -> 17]
(*    {{x -> 2}, {x -> 8}, {x -> 9}, {x -> 15}}    *)